all_task<- cbind(s2r_abs,s2v_abs) %>%
select(sid, frame_effect_r, frame_effect_v, frame_size)
p_df<- perception_abs %>%
ungroup() %>%
select(magnitude, sid) %>%
rename(sub_1 =sid)
all_task<- cbind(all_task,p_df)
all_task<- all_task %>%
select(-sub_1)
all_task<-all_task %>%
rename(vv= frame_effect_v,
oc = frame_effect_r,
perc = magnitude)
across_frames<- perc_x_sacc_df %>%
pivot_wider(names_from = task, values_from = magnitude)
To determine the change in PSE as a function of frame size, we subtracted the PSE for counterclockwise trials from clockwise trials, and then divided that by half.
A negative value indicates that participants PSEs are being
biased in the opposite direction of the tilt of the frame.
| Frame Size | Mean | Median | SD | Min | Max |
|---|---|---|---|---|---|
| Small | 2.11 | 2.00 | 1.15 | -0.27 | 6.35 |
| Medium | 1.91 | 1.71 | 1.12 | 0.15 | 6.68 |
| Large | 1.71 | 1.45 | 1.02 | -0.06 | 4.77 |
| Extra Large | 1.55 | 1.33 | 0.99 | -0.50 | 5.80 |
Perception Task: RFI | |||||||
|---|---|---|---|---|---|---|---|
frame_size | estimate | statistic | p | parameter | Method | Alternative | 95% CI |
175 | 2.11 | 16.44 | < .001*** | 79.00 | One Sample t-test | two.sided | [1.85, 2.37] |
410 | 1.91 | 15.27 | < .001*** | 79.00 | One Sample t-test | two.sided | [1.66, 2.16] |
645 | 1.71 | 14.97 | < .001*** | 79.00 | One Sample t-test | two.sided | [1.48, 1.93] |
880 | 1.55 | 14.03 | < .001*** | 79.00 | One Sample t-test | two.sided | [1.33, 1.77] |
p_mag_anova<- aov(frame_effect_r ~FRAME_SIZE_VAL, data =saccade_to_rod_magnitude)
summary(p_mag_anova)
## Df Sum Sq Mean Sq F value Pr(>F)
## FRAME_SIZE_VAL 3 46.9 15.635 9.284 6.7e-06 ***
## Residuals 316 532.2 1.684
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
tukey_p<-tukey_hsd(p_mag_anova)
tukey_p
## # A tibble: 6 × 9
## term group1 group2 null.value estimate conf.low conf.high p.adj
## * <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 FRAME_SIZE_VAL 175 410 0 0.730 0.200 1.26 0.00242
## 2 FRAME_SIZE_VAL 175 645 0 0.992 0.462 1.52 0.0000123
## 3 FRAME_SIZE_VAL 175 880 0 0.851 0.321 1.38 0.000251
## 4 FRAME_SIZE_VAL 410 645 0 0.262 -0.268 0.792 0.578
## 5 FRAME_SIZE_VAL 410 880 0 0.121 -0.409 0.651 0.935
## 6 FRAME_SIZE_VAL 645 880 0 -0.141 -0.671 0.389 0.902
## # ℹ 1 more variable: p.adj.signif <chr>
apa_table(tukey_p)
| term | group1 | group2 | null.value | estimate | conf.low | conf.high | p.adj | p.adj.signif |
|---|---|---|---|---|---|---|---|---|
| FRAME_SIZE_VAL | 175 | 410 | 0.00 | 0.73 | 0.20 | 1.26 | 0.00 | ** |
| FRAME_SIZE_VAL | 175 | 645 | 0.00 | 0.99 | 0.46 | 1.52 | 0.00 | **** |
| FRAME_SIZE_VAL | 175 | 880 | 0.00 | 0.85 | 0.32 | 1.38 | 0.00 | *** |
| FRAME_SIZE_VAL | 410 | 645 | 0.00 | 0.26 | -0.27 | 0.79 | 0.58 | ns |
| FRAME_SIZE_VAL | 410 | 880 | 0.00 | 0.12 | -0.41 | 0.65 | 0.94 | ns |
| FRAME_SIZE_VAL | 645 | 880 | 0.00 | -0.14 | -0.67 | 0.39 | 0.90 | ns |
The results between the table and graph are inconsistent due to different tests being used. I am unsure whether I need to use the Tukey HSD test ( shown in the table above) or if a Holm-Bonferroni correction is more appropriate (used in the violin graph below).
The effect of the frames was quantified by subtracting the mean errors for the counterclockwise-tilted frames from those of the clockwise-tilted frames then halving this value to get a measure of the average effect of a single frame (negative values indicated eye movements that deviated in the direction opposite the tilt of the frame).
| Frame Size | Mean | Median | SD | Min | Max |
|---|---|---|---|---|---|
| Small | 1.47 | 1.31 | 1.63 | -2.77 | 8.74 |
| Medium | 1.23 | 1.01 | 1.75 | -1.84 | 8.34 |
| Large | 1.14 | 1.04 | 1.35 | -1.63 | 5.91 |
| Extra Large | 1.04 | 0.88 | 1.51 | -2.10 | 8.97 |
s2v_ttest_df<-saccade_to_vert_magnitude %>% group_by(FRAME_SIZE_VAL) %>% do(tidy(t.test(.$frame_effect_v)))
nice_table(s2v_ttest_df)
FRAME_SIZE_VAL | estimate | statistic | p | parameter | Method | Alternative | 95% CI |
|---|---|---|---|---|---|---|---|
175 | 1.47 | 8.04 | < .001*** | 79.00 | One Sample t-test | two.sided | [1.11, 1.83] |
410 | 1.23 | 6.29 | < .001*** | 79.00 | One Sample t-test | two.sided | [0.84, 1.62] |
645 | 1.14 | 7.55 | < .001*** | 79.00 | One Sample t-test | two.sided | [0.84, 1.44] |
880 | 1.04 | 6.16 | < .001*** | 79.00 | One Sample t-test | two.sided | [0.70, 1.37] |
vv_mag_anova<- aov(frame_effect_v~FRAME_SIZE_VAL, data =saccade_to_vert_magnitude)
#summary(vv_mag_anova)
tukey_vv<-tukey_hsd(vv_mag_anova)
apa_table(tukey_vv)
| term | group1 | group2 | null.value | estimate | conf.low | conf.high | p.adj | p.adj.signif |
|---|---|---|---|---|---|---|---|---|
| FRAME_SIZE_VAL | 175 | 410 | 0.00 | -0.24 | -0.88 | 0.40 | 0.77 | ns |
| FRAME_SIZE_VAL | 175 | 645 | 0.00 | -0.33 | -0.97 | 0.31 | 0.56 | ns |
| FRAME_SIZE_VAL | 175 | 880 | 0.00 | -0.43 | -1.07 | 0.21 | 0.31 | ns |
| FRAME_SIZE_VAL | 410 | 645 | 0.00 | -0.09 | -0.73 | 0.55 | 0.98 | ns |
| FRAME_SIZE_VAL | 410 | 880 | 0.00 | -0.19 | -0.83 | 0.45 | 0.87 | ns |
| FRAME_SIZE_VAL | 645 | 880 | 0.00 | -0.10 | -0.75 | 0.54 | 0.98 | ns |
## `geom_smooth()` using formula = 'y ~ x'
The effect of the frames was quantified by subtracting the mean errors for the counterclockwise-tilted frames from those of the clockwise-tilted frames then halving this value to get a measure of the average effect of a single frame (negative values indicated eye movements that deviated in the direction opposite the tilt of the frame).
| Frame Size | Mean | Median | SD | Min | Max |
|---|---|---|---|---|---|
| Small | -1.61 | -1.50 | 1.44 | -6.47 | 4.51 |
| Medium | -0.88 | -0.99 | 1.24 | -4.38 | 2.39 |
| Large | -0.62 | -0.58 | 1.35 | -4.01 | 4.02 |
| Extra Large | -0.76 | -0.70 | 1.14 | -4.76 | 2.57 |
FRAME_SIZE_VAL | estimate | statistic | p | parameter | Method | Alternative | 95% CI |
|---|---|---|---|---|---|---|---|
175 | -1.61 | -9.98 | < .001*** | 79.00 | One Sample t-test | two.sided | [-1.93, -1.29] |
410 | -0.88 | -6.36 | < .001*** | 79.00 | One Sample t-test | two.sided | [-1.15, -0.60] |
645 | -0.62 | -4.09 | < .001*** | 79.00 | One Sample t-test | two.sided | [-0.92, -0.32] |
880 | -0.76 | -5.94 | < .001*** | 79.00 | One Sample t-test | two.sided | [-1.01, -0.50] |
## Df Sum Sq Mean Sq F value Pr(>F)
## FRAME_SIZE_VAL 3 46.9 15.635 9.284 6.7e-06 ***
## Residuals 316 532.2 1.684
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
| term | group1 | group2 | null.value | estimate | conf.low | conf.high | p.adj | p.adj.signif |
|---|---|---|---|---|---|---|---|---|
| FRAME_SIZE_VAL | Small | Medium | 0.00 | -0.73 | -1.26 | -0.20 | 0.00 | ** |
| FRAME_SIZE_VAL | Small | Large | 0.00 | -0.99 | -1.52 | -0.46 | 0.00 | **** |
| FRAME_SIZE_VAL | Small | Extra Large | 0.00 | -0.85 | -1.38 | -0.32 | 0.00 | *** |
| FRAME_SIZE_VAL | Medium | Large | 0.00 | -0.26 | -0.79 | 0.27 | 0.58 | ns |
| FRAME_SIZE_VAL | Medium | Extra Large | 0.00 | -0.12 | -0.65 | 0.41 | 0.94 | ns |
| FRAME_SIZE_VAL | Large | Extra Large | 0.00 | 0.14 | -0.39 | 0.67 | 0.90 | ns
|
So far the perceptual and orientation contrast effect were reported as negative numbers, indicating that the perceptual response or saccade erred in the opposite direction of the tilt of the frame. However, it should be noted that for the purpose of making an additive comparison between summed saccade tasks and the perceptual response, we used the inverse value of the OC effect.
## Effect sizes were labelled following Funder's (2019) recommendations.
##
## The Pearson's product-moment correlation between across_frames$perception and
## across_frames$combined_saccade is positive, statistically significant, and very
## large (r = 0.43, 95% CI [0.33, 0.51], t(318) = 8.45, p < .001)
## `geom_smooth()` using formula = 'y ~ x'
##
## Pearson's product-moment correlation
##
## data: comb_sacc_perc_175$perception and comb_sacc_perc_175$combined_saccade
## t = 1.2689, df = 78, p-value = 0.2083
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.08000506 0.35096232
## sample estimates:
## cor
## 0.1422117
##
## Pearson's product-moment correlation
##
## data: comb_sacc_perc_410$perception and comb_sacc_perc_410$combined_saccade
## t = 4.9876, df = 78, p-value = 3.619e-06
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.3049679 0.6420802
## sample estimates:
## cor
## 0.4917352
##
## Pearson's product-moment correlation
##
## data: comb_sacc_perc_645$perception and comb_sacc_perc_645$combined_saccade
## t = 4.9228, df = 78, p-value = 4.662e-06
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.2991548 0.6383051
## sample estimates:
## cor
## 0.48687
##
## Pearson's product-moment correlation
##
## data: comb_sacc_perc_880$perception and comb_sacc_perc_880$combined_saccade
## t = 5.7131, df = 78, p-value = 1.935e-07
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.3672545 0.6815287
## sample estimates:
## cor
## 0.543144
## Effect sizes were labelled following Funder's (2019) recommendations.
##
## The Pearson's product-moment correlation between across_frames$perception and
## across_frames$combined_saccade is positive, statistically significant, and very
## large (r = 0.43, 95% CI [0.33, 0.51], t(318) = 8.45, p < .001)
## `geom_smooth()` using formula = 'y ~ x'
Perception and Saccade-to-Vertical
## `geom_smooth()` using formula = 'y ~ x'
Perception and Saccade-to-Rod
## `geom_smooth()` using formula = 'y ~ x'
##
## Pearson's product-moment correlation
##
## data: s2r_perc_175$perception and s2r_perc_175$s2r
## t = -2.1634, df = 78, p-value = 0.03357
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.43490358 -0.01920867
## sample estimates:
## cor
## -0.2379214
##
## Pearson's product-moment correlation
##
## data: s2r_perc_410$perception and s2r_perc_410$s2r
## t = -2.6151, df = 78, p-value = 0.0107
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.47405942 -0.06846902
## sample estimates:
## cor
## -0.2839148
##
## Pearson's product-moment correlation
##
## data: s2r_perc_645$perception and s2r_perc_645$s2r
## t = -3.4645, df = 78, p-value = 0.0008661
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5414599 -0.1581624
## sample estimates:
## cor
## -0.3651887
##
## Pearson's product-moment correlation
##
## data: s2r_perc_880$perception and s2r_perc_880$s2r
## t = -2.6239, df = 78, p-value = 0.01045
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.47480242 -0.06942329
## sample estimates:
## cor
## -0.2847961
#two way anova task X frame size summary stats
task_by_frame_long %>%
group_by(frame_size,task) %>%
get_summary_stats(magnitude,type = "mean_sd")
## # A tibble: 8 × 6
## frame_size task variable n mean sd
## <fct> <fct> <fct> <dbl> <dbl> <dbl>
## 1 175 vv magnitude 80 1.47 1.63
## 2 175 oc magnitude 80 1.61 1.44
## 3 410 vv magnitude 80 1.23 1.75
## 4 410 oc magnitude 80 0.88 1.24
## 5 645 vv magnitude 80 1.14 1.35
## 6 645 oc magnitude 80 0.618 1.35
## 7 880 vv magnitude 80 1.04 1.51
## 8 880 oc magnitude 80 0.759 1.14
#box plot
task_frame_bxp<- ggboxplot(
task_by_frame_long, x = "frame_size", y = "magnitude", color = "task", pallet ="jco")
task_frame_bxp
For each frame size a hierarchical design was employed using two models: 1) model 1 predicted the overall RFI magnitude (measured by the perception task) from the visuovestibular effect (measured by the saccade-to-vertical task) and 2) model 2 predicted the overall RFI magnitude from visuovestibular effect and the orientation contrast effect (measured by the saccade-to-rod task).
##
## Call:
## lm(formula = perc ~ vv, data = df_small)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.4004 -0.7165 -0.1283 0.4315 4.2230
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.12753 0.17419 12.214 <2e-16 ***
## vv -0.01199 0.07954 -0.151 0.881
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.155 on 78 degrees of freedom
## Multiple R-squared: 0.0002913, Adjusted R-squared: -0.01253
## F-statistic: 0.02273 on 1 and 78 DF, p-value: 0.8805
##
## Call:
## lm(formula = perc ~ vv + oc, data = df_small)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.4789 -0.6643 -0.1876 0.3187 4.2826
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.83034 0.21902 8.357 2.08e-12 ***
## vv -0.01792 0.07779 -0.230 0.8184
## oc 0.19003 0.08810 2.157 0.0341 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.129 on 77 degrees of freedom
## Multiple R-squared: 0.05726, Adjusted R-squared: 0.03277
## F-statistic: 2.338 on 2 and 77 DF, p-value: 0.1033
## [1] 0.05696534
## Analysis of Variance Table
##
## Model 1: perc ~ vv
## Model 2: perc ~ vv + oc
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 78 104.12
## 2 77 98.19 1 5.9331 4.6527 0.03412 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
| Model 1 | Model 2 | |
|---|---|---|
| (Intercept) | 2.128 | 1.830 |
| (0.174) | (0.219) | |
| vv | -0.012 | -0.018 |
| (0.080) | (0.078) | |
| oc | 0.190 | |
| (0.088) | ||
| Num.Obs. | 80 | 80 |
| R2 | 0.000 | 0.057 |
| R2 Adj. | -0.013 | 0.033 |
| AIC | 254.1 | 251.4 |
| BIC | 261.3 | 260.9 |
| Log.Lik. | -124.057 | -121.710 |
| RMSE | 1.14 | 1.11 |
oc_small<- lm(perc~ oc, df_small)
summary(oc_small)
##
## Call:
## lm(formula = perc ~ oc, data = df_small)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.4518 -0.6510 -0.2152 0.3203 4.3107
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.80516 0.18865 9.569 8.55e-15 ***
## oc 0.18931 0.08751 2.163 0.0336 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.122 on 78 degrees of freedom
## Multiple R-squared: 0.05661, Adjusted R-squared: 0.04451
## F-statistic: 4.68 on 1 and 78 DF, p-value: 0.03357
####Medium Frame
##
## Call:
## lm(formula = perc ~ vv, data = df_medium)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.7622 -0.6009 -0.1230 0.4030 3.2499
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.57513 0.13952 11.290 < 2e-16 ***
## vv 0.27040 0.06549 4.129 9.06e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.019 on 78 degrees of freedom
## Multiple R-squared: 0.1794, Adjusted R-squared: 0.1689
## F-statistic: 17.05 on 1 and 78 DF, p-value: 9.057e-05
##
## Call:
## lm(formula = perc ~ vv + oc, data = df_medium)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.92902 -0.56106 -0.08099 0.47815 3.13629
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.39053 0.15335 9.068 8.87e-14 ***
## vv 0.25768 0.06352 4.056 0.000118 ***
## oc 0.22763 0.08988 2.533 0.013356 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.985 on 77 degrees of freedom
## Multiple R-squared: 0.2425, Adjusted R-squared: 0.2228
## F-statistic: 12.32 on 2 and 77 DF, p-value: 2.273e-05
## [1] 0.0631005
## Analysis of Variance Table
##
## Model 1: perc ~ vv
## Model 2: perc ~ vv + oc
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 78 80.926
## 2 77 74.703 1 6.2227 6.4141 0.01336 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
| Model 1 | Model 2 | |
|---|---|---|
| (Intercept) | 1.575 | 1.391 |
| (0.140) | (0.153) | |
| vv | 0.270 | 0.258 |
| (0.065) | (0.064) | |
| oc | 0.228 | |
| (0.090) | ||
| Num.Obs. | 80 | 80 |
| R2 | 0.179 | 0.242 |
| R2 Adj. | 0.169 | 0.223 |
| AIC | 234.0 | 229.5 |
| BIC | 241.1 | 239.1 |
| Log.Lik. | -113.975 | -110.775 |
| RMSE | 1.01 | 0.97 |
oc_medium<- lm(perc~ oc, df_medium)
summary(oc_medium)
##
## Call:
## lm(formula = perc ~ oc, data = df_medium)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.5927 -0.6444 -0.2625 0.3698 4.1965
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.68232 0.14824 11.349 <2e-16 ***
## oc 0.25647 0.09807 2.615 0.0107 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.078 on 78 degrees of freedom
## Multiple R-squared: 0.08061, Adjusted R-squared: 0.06882
## F-statistic: 6.839 on 1 and 78 DF, p-value: 0.0107
####Large Frame
##
## Call:
## lm(formula = perc ~ vv, data = df_large)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.8761 -0.6915 -0.1754 0.5270 3.5536
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.37309 0.13883 9.890 2.05e-15 ***
## vv 0.29264 0.07861 3.723 0.000371 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9464 on 78 degrees of freedom
## Multiple R-squared: 0.1509, Adjusted R-squared: 0.14
## F-statistic: 13.86 on 1 and 78 DF, p-value: 0.0003706
##
## Call:
## lm(formula = perc ~ vv + oc, data = df_large)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.6401 -0.5876 -0.2332 0.2946 3.9705
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.28410 0.13581 9.455 1.59e-14 ***
## vv 0.24787 0.07650 3.240 0.00177 **
## oc 0.22699 0.07681 2.955 0.00415 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9027 on 77 degrees of freedom
## Multiple R-squared: 0.2373, Adjusted R-squared: 0.2175
## F-statistic: 11.98 on 2 and 77 DF, p-value: 2.948e-05
## [1] 0.08649254
## Analysis of Variance Table
##
## Model 1: perc ~ vv
## Model 2: perc ~ vv + oc
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 78 69.863
## 2 77 62.747 1 7.1162 8.7326 0.004146 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
| Model 1 | Model 2 | |
|---|---|---|
| (Intercept) | 1.373 | 1.284 |
| (0.139) | (0.136) | |
| vv | 0.293 | 0.248 |
| (0.079) | (0.076) | |
| oc | 0.227 | |
| (0.077) | ||
| Num.Obs. | 80 | 80 |
| R2 | 0.151 | 0.237 |
| R2 Adj. | 0.140 | 0.218 |
| AIC | 222.2 | 215.6 |
| BIC | 229.3 | 225.1 |
| Log.Lik. | -108.096 | -103.798 |
| RMSE | 0.93 | 0.89 |
oc_large<- lm(perc~ oc, df_large)
summary(oc_large)
##
## Call:
## lm(formula = perc ~ oc, data = df_large)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.5026 -0.7240 -0.3182 0.5357 3.4002
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.53706 0.11769 13.060 < 2e-16 ***
## oc 0.27628 0.07974 3.465 0.000866 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9561 on 78 degrees of freedom
## Multiple R-squared: 0.1334, Adjusted R-squared: 0.1223
## F-statistic: 12 on 1 and 78 DF, p-value: 0.0008661
####Extra Large Frame
##
## Call:
## lm(formula = perc ~ vv, data = df_xl)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.55711 -0.62980 -0.02815 0.50862 2.08057
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.18155 0.11387 10.376 2.40e-16 ***
## vv 0.35265 0.06248 5.644 2.57e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.837 on 78 degrees of freedom
## Multiple R-squared: 0.29, Adjusted R-squared: 0.2809
## F-statistic: 31.86 on 1 and 78 DF, p-value: 2.569e-07
##
## Call:
## lm(formula = perc ~ vv + oc, data = df_xl)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.73611 -0.57671 0.00541 0.53652 2.24999
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.09815 0.12229 8.980 1.31e-13 ***
## vv 0.32691 0.06345 5.152 1.93e-06 ***
## oc 0.14516 0.08372 1.734 0.0869 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8264 on 77 degrees of freedom
## Multiple R-squared: 0.3167, Adjusted R-squared: 0.2989
## F-statistic: 17.84 on 2 and 77 DF, p-value: 4.294e-07
## [1] 0.02668074
## Analysis of Variance Table
##
## Model 1: perc ~ vv
## Model 2: perc ~ vv + oc
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 78 54.640
## 2 77 52.586 1 2.0533 3.0066 0.08693 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
| Model 1 | Model 2 | |
|---|---|---|
| (Intercept) | 1.182 | 1.098 |
| (0.114) | (0.122) | |
| vv | 0.353 | 0.327 |
| (0.062) | (0.063) | |
| oc | 0.145 | |
| (0.084) | ||
| Num.Obs. | 80 | 80 |
| R2 | 0.290 | 0.317 |
| R2 Adj. | 0.281 | 0.299 |
| AIC | 202.5 | 201.5 |
| BIC | 209.7 | 211.0 |
| Log.Lik. | -98.264 | -96.732 |
| RMSE | 0.83 | 0.81 |
oc_xl<- lm(perc~ oc, df_xl)
summary(oc_xl)
##
## Call:
## lm(formula = perc ~ oc, data = df_xl)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.7607 -0.6438 -0.1995 0.5181 3.7649
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.36114 0.12804 10.630 <2e-16 ***
## oc 0.24608 0.09378 2.624 0.0105 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9522 on 78 degrees of freedom
## Multiple R-squared: 0.08111, Adjusted R-squared: 0.06933
## F-statistic: 6.885 on 1 and 78 DF, p-value: 0.01045